1
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Let $$\Delta$$, $$\nabla$$ $$\in$$ {$$\wedge$$, $$\vee$$} be such that p $$\nabla$$ q $$\Rightarrow$$ ((p $$\Delta$$ q) $$\nabla$$ r) is a tautology. Then (p $$\nabla$$ q) $$\Delta$$ r is logically equivalent to :

A
(p $$\Delta$$ r) $$\vee$$ q
B
(p $$\Delta$$ r) $$\wedge$$ q
C
(p $$\wedge$$ r) $$\Delta$$ q
D
(p $$\nabla$$ r) $$\wedge$$ q
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

The negation of the Boolean expression (($$\sim$$ q) $$\wedge$$ p) $$\Rightarrow$$ (($$\sim$$ p) $$\vee$$ q) is logically equivalent to :

A
$$p \Rightarrow q$$
B
$$q \Rightarrow p$$
C
$$\sim (p \Rightarrow q)$$
D
$$\sim (q \Rightarrow p)$$
3
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Consider the following two propositions:

$$P1: \sim (p \to \sim q)$$

$$P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)$$

If the proposition $$p \to (( \sim p) \vee q)$$ is evaluated as FALSE, then :

A
P1 is TRUE and P2 is FALSE
B
P1 is FALSE and P2 is TRUE
C
Both P1 and P2 are FALSE
D
Both P1 and P2 are TRUE
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Consider the following statements:

A : Rishi is a judge.

B : Rishi is honest.

C : Rishi is not arrogant.

The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

A
B $$\to$$ (A $$\vee$$ C)
B
($$\sim$$B) $$\wedge$$ (A $$\wedge$$ C)
C
B $$\to$$ (($$\sim$$A) $$\vee$$ ($$\sim$$C))
D
B $$\to$$ (A $$\wedge$$ C)
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